File with USAA or other drivers Allstate?

My car was parked in a parking lot when another car backed into my rear passenger door, it is pretty dented but damage is right in the middle so it opens and closes just fine. I got the other drivers insurance and based on the fact my car was parked without me in it, it seems pretty clear-cut that the other driver is at fault.

Im confused on if I should file with my insurance (USAA) or the other drivers insurance (Allstate)? Seems like USAA will be quicker but Allstate will be cheaper (not needing to pay the deductible). Is the deductible reimbursed in a case like this? The other driver does live in another state.

Also there was a carseat ib the car on the rear passenger side if that comes into play and makes a difference at all.